Commit eb72df7b authored by Frédéric Karamé's avatar Frédéric Karamé
Browse files

computes the proposal distribution during the importance sampling step for...

computes the proposal distribution during the importance sampling step for gaussian-mixture filters. Fix many bugs.
parent ab2ae38e
function [StateMuPrior,StateSqrtPPrior,StateWeightsPrior,StateMuPost,StateSqrtPPost,StateWeightsPost] =...
gaussian_mixture_filter_bank(ReducedForm,obs,StateMu,StateSqrtP,StateWeights,...
StructuralShocksMu,StructuralShocksSqrtP,StructuralShocksWeights,...
ObservationShocksMu,ObservationShocksSqrtP,ObservationShocksWeights,...
H,H_lower_triangular_cholesky,normfactO,DynareOptions)
%
% Computes the proposal with a gaussian approximation for importance
% sampling
% This proposal is a gaussian distribution calculated à la Kalman
%
% INPUTS
% reduced_form_model [structure] Matlab's structure describing the reduced form model.
% reduced_form_model.measurement.H [double] (pp x pp) variance matrix of measurement errors.
% reduced_form_model.state.Q [double] (qq x qq) variance matrix of state errors.
% reduced_form_model.state.dr [structure] output of resol.m.
% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
%
% OUTPUTS
% LIK [double] scalar, likelihood
% lik [double] vector, density of observations in each period.
%
% REFERENCES
%
% NOTES
% The vector "lik" is used to evaluate the jacobian of the likelihood.
% Copyright (C) 2009-2012 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
persistent init_flag2 mf0 mf1 %nodes3 weights3 weights_c3
persistent number_of_state_variables number_of_observed_variables
persistent number_of_structural_innovations
% Set local state space model (first-order approximation).
ghx = ReducedForm.ghx;
ghu = ReducedForm.ghu;
% Set local state space model (second-order approximation).
ghxx = ReducedForm.ghxx;
ghuu = ReducedForm.ghuu;
ghxu = ReducedForm.ghxu;
if any(any(isnan(ghx))) || any(any(isnan(ghu))) || any(any(isnan(ghxx))) || any(any(isnan(ghuu))) || any(any(isnan(ghxu))) || ...
any(any(isinf(ghx))) || any(any(isinf(ghu))) || any(any(isinf(ghxx))) || any(any(isinf(ghuu))) || any(any(isinf(ghxu))) ...
any(any(abs(ghx)>1e4)) || any(any(abs(ghu)>1e4)) || any(any(abs(ghxx)>1e4)) || any(any(abs(ghuu)>1e4)) || any(any(abs(ghxu)>1e4))
ghx
ghu
ghxx
ghuu
ghxu
end
constant = ReducedForm.constant;
state_variables_steady_state = ReducedForm.state_variables_steady_state;
% Set persistent variables.
if isempty(init_flag2)
mf0 = ReducedForm.mf0;
mf1 = ReducedForm.mf1;
number_of_state_variables = length(mf0);
number_of_observed_variables = length(mf1);
number_of_structural_innovations = length(ReducedForm.Q);
init_flag2 = 1;
end
numb = number_of_state_variables+number_of_structural_innovations ;
if strcmpi(DynareOptions.particle.IS_approximation_method,'quadrature')
[nodes3,weights3] = nwspgr('GQN',numb,DynareOptions.particle.smolyak_accuracy) ;
weights_c3 = weights3 ;
end
if strcmpi(DynareOptions.particle.IS_approximation_method,'cubature')
[nodes3,weights3] = spherical_radial_sigma_points(numb) ;
weights_c3 = weights3 ;
end
if strcmpi(DynareOptions.particle.IS_approximation_method,'unscented')
[nodes3,weights3,weights_c3] = unscented_sigma_points(numb,DynareOptions) ;
end
epsilon = bsxfun(@plus,StructuralShocksSqrtP*nodes3(:,number_of_state_variables+1:number_of_state_variables+number_of_structural_innovations)',StructuralShocksMu) ;
StateVectors = bsxfun(@plus,StateSqrtP*nodes3(:,1:number_of_state_variables)',StateMu);
%ObservationShocks = bsxfun(@plus,ObservationShocksSqrtP*nodes3(:,1+number_of_state_variables+number_of_structural_innovations:number_of_state_variables+number_of_structural_innovations+number_of_observed_variables)',ObservationShocksMu) ;
yhat = bsxfun(@minus,StateVectors,state_variables_steady_state) ;
tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2);
PredictedStateMean = tmp(mf0,:)*weights3;
PredictedObservedMean = tmp(mf1,:)*weights3;
if strcmpi(DynareOptions.particle.IS_approximation_method,'cubature')
PredictedStateMean = sum(PredictedStateMean,2) ;
PredictedObservedMean = sum(PredictedObservedMean,2) ;
dState = (bsxfun(@minus,tmp(mf0,:),PredictedStateMean)').*sqrt(weights3) ;
dObserved = (bsxfun(@minus,tmp(mf1,:),PredictedObservedMean)').*sqrt(weights3);
PredictedStateVariance = dState'*dState;
big_mat = [dObserved dState ; [H_lower_triangular_cholesky zeros(number_of_observed_variables,number_of_state_variables)] ] ;
[mat1,mat] = qr2(big_mat) ;
mat = mat' ;
clear('mat1');
PredictedObservedVarianceSquareRoot = mat(1:number_of_observed_variables,1:number_of_observed_variables) ;
CovarianceObservedStateSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),1:number_of_observed_variables) ;
StateVectorVarianceSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),number_of_observed_variables+(1:number_of_state_variables)) ;
iPredictedObservedVarianceSquareRoot = inv(PredictedObservedVarianceSquareRoot);
iPredictedObservedVariance = iPredictedObservedVarianceSquareRoot'*iPredictedObservedVarianceSquareRoot ;
sqrdet = 1/sqrt(det(iPredictedObservedVariance)) ;
PredictionError = obs - PredictedObservedMean ;
StateVectorMean = PredictedStateMean + CovarianceObservedStateSquareRoot*iPredictedObservedVarianceSquareRoot*PredictionError;
end
if strcmpi(DynareOptions.particle.IS_approximation_method,'quadrature') || ...
strcmpi(DynareOptions.particle.IS_approximation_method,'unscented')
dState = bsxfun(@minus,tmp(mf0,:),PredictedStateMean);
dObserved = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean);
PredictedStateVariance = dState*diag(weights_c3)*dState';
PredictedObservedVariance = dObserved*diag(weights_c3)*dObserved' + H;
PredictedStateAndObservedCovariance = dState*diag(weights_c3)*dObserved';
sqrdet = sqrt(det(PredictedObservedVariance)) ;
iPredictedObservedVariance = inv(PredictedObservedVariance);
PredictionError = obs - PredictedObservedMean;
KalmanFilterGain = PredictedStateAndObservedCovariance*iPredictedObservedVariance;
StateVectorMean = PredictedStateMean + KalmanFilterGain*PredictionError;
StateVectorVariance = PredictedStateVariance - KalmanFilterGain*PredictedObservedVariance*KalmanFilterGain';
StateVectorVariance = .5*(StateVectorVariance+StateVectorVariance');
StateVectorVarianceSquareRoot = reduced_rank_cholesky(StateVectorVariance)';
end
data_lik_GM_g = exp(-0.5*PredictionError'*iPredictedObservedVariance*PredictionError)/abs(normfactO*sqrdet) + 1e-99;
StateMuPrior = PredictedStateMean ;
StateSqrtPPrior = reduced_rank_cholesky(PredictedStateVariance)' ;
StateWeightsPrior = StateWeights*StructuralShocksWeights ;
StateMuPost = StateVectorMean ;
StateSqrtPPost = StateVectorVarianceSquareRoot ;
StateWeightsPost = StateWeightsPrior*ObservationShocksWeights*data_lik_GM_g ;
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